Defining the scalar moment of a seismic source with a general moment tensor

We compare several published definitions of the scalar moment M0, a measure of the size of a seismic disturbance derived from the second-order seismic moment tensor M (with eigenvalues m1 ≥ m3 ≥ m2). While arbitrary, a useful definition is in terms of a total moment, MT0 = MI + MD, where MI = |M|, with M = (m1 + m2 + m3)/3, is the isotropic moment, and MD = max(|mj − M|; j = 1, 2, 3), is the deviatoric moment. This definition is consistent with other definitions of M0 if M is a double couple. This definition also gives physically appealing and simple results for the explosion and crack sources. Furthermore, our definitions of MT0, MI and MD are in accord with the parameterization of the moment tensor into a deviatoric part (represented by T which lies in [−1,1]) and a volumetric part (represented by k which lies in [−1, 1]) proposed by Hudson et al. (1989).